1. In a saucepan, combine the eggs with generously salted water to cover by at least an inch and a half. Bring to a boil over medium-high heat, reduce the heat to low, and gently simmer for 12 minutes. Meanwhile, fill a large bowl with ice water. Transfer the eggs to the water and cool for 8−10 minutes. Crack the eggs at the broad end and in a few other places and carefully peel. Once peeled, use them right away or refrigerate for up to three days.

2. Cut the eggs in half lengthwise. Carefully remove the yolks to a bowl. Lay the egg whites cut side up on a platter. (If not filling them until the following day, place them cut side down on a plate, cover with plastic wrap, and refrigerate.)

3. Mash the yolks with the goat cheese, mayonnaise, shallot, jalapeños, pickled juice, Dijon mustard, and cumin, and stir until smooth. If desired, season with salt, and add more jalapeños or juice, if desired. Using a pastry tube fitted with a wide star tip, or a small spatula, fill the eggs. Serve on a platter sprinkled with Pimentón de la Vera. Garnish with arugula and cherry tomatoes, if desired.